Details

Time bar (total: 19.9s)

sample186.0ms

Algorithm
intervals
Results
93.0ms88×body1280valid
46.0ms61×body640valid
14.0ms28×body320valid
9.0ms69×body80valid
3.0ms10×body160valid

simplify666.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
03250
17450
218747
359347
4197147
done500047

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
1.7b
(- (cos x) (cos y))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
184×add-sqr-sqrt
183×prod-diff
172×*-un-lft-identity
164×add-cube-cbrt
110×times-frac
82×distribute-rgt-in distribute-lft-in
14×sqrt-prod
12×associate-*r* div-inv
11×pow1 add-exp-log add-cbrt-cube
10×associate-*r/
9×flip3-- flip--
8×add-log-exp
7×associate-*l* difference-of-squares
6×sub-neg fma-neg
4×expm1-log1p-u frac-times pow-prod-down prod-exp cbrt-unprod log1p-expm1-u distribute-lft-out--
2×diff-log associate-*l/ *-commutative unswap-sqr
1×diff-cos
Counts
4 → 291
Calls
4 calls:
65.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
40.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms
(- 3.0 (sqrt 5.0))
4.0ms
(- (cos x) (cos y))

series271.0ms

Counts
4 → 10
Calls
4 calls:
128.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
87.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
57.0ms
(- (cos x) (cos y))

simplify503.0ms

Counts
301 → 301
Iterations

Useful iterations: done (488.0ms)

IterNodesCost
073212252
1173510935
done500010884

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (fma (- (cos x) (cos y)) (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) 2.0) 3.0) (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
0.3b
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.7b
(- (cos x) (cos y))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
209×add-sqr-sqrt
199×*-un-lft-identity
193×add-cube-cbrt
185×times-frac
165×prod-diff
82×distribute-rgt-in distribute-lft-in
17×div-inv
16×add-exp-log add-cbrt-cube
13×associate-/l*
12×associate-*r*
11×pow1
10×associate-*r/
8×flip3-- flip--
7×associate-*l*
6×add-log-exp
5×sub-neg difference-of-squares
4×expm1-log1p-u frac-times pow-prod-down prod-exp sqrt-prod cbrt-unprod log1p-expm1-u
3×cbrt-undiv fma-neg div-exp associate-/r* distribute-lft-out--
2×associate-*l/ *-commutative unswap-sqr
1×frac-2neg diff-log clear-num diff-cos associate-/l/
Counts
4 → 325
Calls
4 calls:
6.0ms
(/ (/ (fma (- (cos x) (cos y)) (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) 2.0) 3.0) (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
66.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
38.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms
(- (cos x) (cos y))

series1.7s

Counts
4 → 12
Calls
4 calls:
1.4s
(/ (/ (fma (- (cos x) (cos y)) (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) 2.0) 3.0) (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
137.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
90.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
51.0ms
(- (cos x) (cos y))

simplify633.0ms

Counts
337 → 337
Iterations

Useful iterations: done (614.0ms)

IterNodesCost
088018227
1214817028
done500016985

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (fma (- (cos x) (cos y)) (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) 2.0) (* (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
0.3b
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.7b
(- (cos x) (cos y))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
169×add-sqr-sqrt
165×prod-diff
159×*-un-lft-identity
153×add-cube-cbrt
113×times-frac
82×distribute-rgt-in distribute-lft-in
16×add-exp-log add-cbrt-cube
13×div-inv
12×associate-*r*
11×pow1
10×associate-*r/
8×flip3-- flip--
7×associate-*l*
6×add-log-exp
5×sub-neg prod-exp cbrt-unprod difference-of-squares
4×expm1-log1p-u frac-times pow-prod-down sqrt-prod log1p-expm1-u
3×fma-neg associate-/l* distribute-lft-out--
2×cbrt-undiv div-exp associate-*l/ *-commutative unswap-sqr
1×frac-2neg diff-log clear-num associate-/r* diff-cos
Counts
4 → 276
Calls
4 calls:
3.0ms
(/ (fma (- (cos x) (cos y)) (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) 2.0) (* (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
66.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
40.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms
(- (cos x) (cos y))

series1.7s

Counts
4 → 12
Calls
4 calls:
1.4s
(/ (fma (- (cos x) (cos y)) (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) 2.0) (* (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
134.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
90.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
58.0ms
(- (cos x) (cos y))

simplify605.0ms

Counts
288 → 288
Iterations

Useful iterations: done (586.0ms)

IterNodesCost
077913518
1191712365
done500012318

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 16.0)
1.0b
(cbrt 16.0)
1.7b
(- (cos x) (cos y))
59.6b
(fma (- (/ (cbrt (sin y)) (cbrt 16.0))) (/ (* (cbrt (sin y)) (cbrt (sin y))) (* (cbrt 16.0) (cbrt 16.0))) (* (/ (cbrt (sin y)) (cbrt 16.0)) (/ (* (cbrt (sin y)) (cbrt (sin y))) (* (cbrt 16.0) (cbrt 16.0)))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt *-un-lft-identity
13×add-cube-cbrt
9×prod-diff
6×cbrt-prod add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×fma-neg
2×pow1/3
1×sub-neg flip3-- diff-log flip-- fma-udef diff-cos distribute-lft-out-- difference-of-squares
Counts
4 → 65
Calls
4 calls:
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
4.0ms
(- (cos x) (cos y))
0.0ms
(fma (- (/ (cbrt (sin y)) (cbrt 16.0))) (/ (* (cbrt (sin y)) (cbrt (sin y))) (* (cbrt 16.0) (cbrt 16.0))) (* (/ (cbrt (sin y)) (cbrt 16.0)) (/ (* (cbrt (sin y)) (cbrt (sin y))) (* (cbrt 16.0) (cbrt 16.0)))))

series419.0ms

Counts
4 → 8
Calls
4 calls:
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
57.0ms
(- (cos x) (cos y))
362.0ms
(fma (- (/ (cbrt (sin y)) (cbrt 16.0))) (/ (* (cbrt (sin y)) (cbrt (sin y))) (* (cbrt 16.0) (cbrt 16.0))) (* (/ (cbrt (sin y)) (cbrt 16.0)) (/ (* (cbrt (sin y)) (cbrt (sin y))) (* (cbrt 16.0) (cbrt 16.0)))))

simplify1.7s

Counts
73 → 73
Iterations

Useful iterations: 3 (373.0ms)

IterNodesCost
01411351
12861233
2811746
33516655
done5000655

prune608.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes199.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
044116
158116
262116
364116
done64116

end0.0ms

sample5.4s

Algorithm
intervals
Results
3.1s2801×body1280valid
1.3s1817×body640valid
350.0ms726×body320valid
321.0ms2321×body80valid
114.0ms335×body160valid